To graph the equation \( 9 - x = \frac{3}{2}y \), we first need to rearrange it into slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the given equation:
\[ 9 - x = \frac{3}{2}y \]
We can rearrange this to solve for \( y \):
- Add \( x \) to both sides:
\[ 9 = x + \frac{3}{2}y \]
- Subtract \( x \) from both sides:
\[ 9 - x = \frac{3}{2}y \]
- Now, multiply both sides by \( \frac{2}{3} \) to isolate \( y \):
\[ y = \frac{2}{3}(9 - x) \]
- Distributing \( \frac{2}{3} \):
\[ y = \frac{18}{3} - \frac{2}{3}x \]
\[ y = 6 - \frac{2}{3}x \]
Now we have the equation in slope-intercept form \( y = -\frac{2}{3}x + 6 \).
From this form, we see that the slope \( m = -\frac{2}{3} \) and the y-intercept \( b = 6 \). Thus, the line crosses the y-axis at the point \( (0, 6) \).
To find another point on the line, we can plug in a value for \( x \). Let's use \( x = 3 \):
\[ y = 6 - \frac{2}{3}(3) = 6 - 2 = 4 \]
So, we have another point at \( (3, 4) \).
We can now plot the two points \( (0, 6) \) and \( (3, 4) \) on a coordinate plane, and draw a line through them.
Based on the descriptions given, the third response fits this graphing description with the plotted points being \( (0, 6) \) and \( (3, 4) \):
An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at \( (0, 6) \) and \( (3, 4) \).
This response matches the analyzed slope-intercept form and points accurately.